To be fair, Khan had 6 months of Ceti Alpha 6 available to him before it exploded. So it's plausible he could have soaked up knowledge there. However, there's a danger of me sounding like an apologist here, when continuity has never been a strong part of Trek.
Something else I really liked about Wrath of Khan was that the inside of the Enterprise looked more like a ship: corridors were narrow and angled, and there was curvature on the walls of Kirk's cabin. Subtle details that Trek is not famous for, especially when the Enterprise normally looks like a spacious luxury hotel rather than a naval vessel or analogue of one.
ADDED: Oh! And something interesting - when the Enterprise entered the Mutara Nebula and the screens became disrupted, my youngest couldn't understand why that was happening. Being a child of the digital age she had no idea what static interference was!
Nothing dates faster than our vision of the future. Nick Myer was annoyed that he wasn't allowed to show people smoking on the Bridge of the Enterprise as he felt it was unrealistic. Flash forward a couple of decades and smoking's been banned in most public places.